(342h) Optimization of Multi-Product Multi-Purpose Batch Plants Using Meta-Heuristic Genetic Algorithms

Batch processes have been used in the industrial production of chemicals for a long time. With the growth of specialty chemicals and other small-scale production, batch production has seen a resurgence, and finding an optimal schedule to run multi-product, multi-purpose batch chemical plants is crucial to maintaining a competitive edge in those settings. However, the coupled nature of these plants as well as the time dependency of batch processes inherently adds a level of complexity that is not found in continuous processes [1]. Several mathematical models based on exact methods [2]–[4] have been proposed to describe and optimize batch process schedules, both in discretized and continuous time scales. These methodologies can be used to identify schedules with guaranteed optimality consistently, but only for small instances relatively to what would be considered instances of industrial relevance. In order to improve tractability, recent works have considered novel integrated scheduling and dynamic optimization [5], tightened valid inequality bounds [6], utilized rolling horizons [7], [8] and implemented models for parallel processes [9]. These works have been instrumental in the development of the field. Nonetheless, as is common with mathematical programming approaches, the exploding combinatorial complexity makes these models intractable to solve in a reasonable time period as the problem size and time horizon grow, and the need for fast—even if inexact—algorithms remains.

Meta-heuristic algorithms, such as genetic algorithms, simulated annealing, and tabu search, have been recognized as practical potential approaches to solving these large combinatorial optimization problems. While these methods do not guarantee optimality and are highly non-deterministic in nature, their strong ability to outperform mathematical programming approaches in large complex problems has been showcased several times [10], [11]. However, limited work has been done to address variable batch sizes in multi-product, multi-purpose (MPMP) batch plants.

In this paper, we present a genetic algorithm (GA) based meta-heuristic approach to optimize the production schedules of MPMP batch plants over a given time horizon. A unique chromosome structure is adopted to encode unit allocations, variable batch sizes and continuous time intervals. A dynamic penalization function is used to guide a broad and greedy search during the earlier iterations, transitioning into deep search to produce high quality feasible schedules. When the population of chromosomes are similar, or when the fitness function does not improve with time, the population size is also dynamically increased during runtime to generate more chromosomes to enable search in new solution neighborhoods. This allows for a larger search space while rationalizing the utilization of the given computational time. Our novel GA approach is validated against small-scale benchmark problems commonly used in the exact optimization literature, where we demonstrate its ability to produce optimal solutions within a reasonable time. Furthermore, we generated a collection of new, large-scale state-task-network data sets, which we employed to highlight the algorithm’s performance in optimizing industrially-relevant instances.

References:

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[10] M. Woolway and T. Majozi, “On the application of a metaheuristic suite with parallel implementations for the scheduling of multipurpose batch plants,” Comput. Chem. Eng., vol. 126, pp. 371–390, 2019.

[11] Y. He and C. W. Hui, “Genetic algorithm for large-size multi-stage batch plant scheduling,” Chem. Eng. Sci., 2007.